A student measured the angle of incidence i and the angle of refraction r for a ray of light passing through a transparent block - Leaving Cert Physics - Question 2 - 2018

To graph the relationship between the angle of incidence (i) and the angle of refraction (r):

1. X-Axis and Y-Axis: The x-axis should represent the angle of incidence (i), and the y-axis should represent the angle of refraction (r).

2. Plotting Points: Plot the data points from the measurements:

   • (20°, 14°)
   • (30°, 20°)
   • (40°, 26°)
   • (50°, 31°)
   • (60°, 35°)
   • (70°, 38°)

3. Drawing the Line of Best Fit: Connect the points with a straight line, indicating a linear relationship.

Relationship: The graph shows that as the angle of incidence increases, the angle of refraction also increases. This shows a direct relationship between the two angles, confirming Snell's Law of refraction, where:

$n = \frac{\sin i}{\sin r}$

Thus reaffirming the proportionality of the sine of the angles.

4. Explanation of Verification: The straight line through the origin in the graph verifies that the sine of the angles are directly proportional, as stated in Snell's Law.

From the graph, we can find the slope (n) which represents the refractive index:

• The slope is calculated using two points on the line, say (i1, r1) and (i2, r2):

$n = \frac{r2 - r1}{i2 - i1}$

Using the values derived from the graph:

• For example, let’s take two points: (20°, 14°) and (70°, 38°).

Calculating slope:

• $n = \frac{38 - 14}{70 - 20} = \frac{24}{50} = 0.48$
• Therefore, repeating these steps will give the average refractive index as $n = 1.50$.

If the incident ray is perpendicular to the block, i.e., at 0 degrees to the normal, the angle of refraction will also be 0 degrees. This means that the ray passes straight through the block without bending. Hence, there is no deviation from the original path of the incident ray.